What if they want to bring one in to read between classes?
This latter thing should be fine; it’s voluntary.
Christianity has had difficulty grasping its New Testament place with respect to worldly governments (prior to Christ’s return, of course). And as long as schools remain government organs, this is going to be an inherent problem.
Not that the bible is wrong, or bad, but that it’s not something we want worldly governments to be trying to minister to people. Such ministry tends to decay into self righteous acts of entities that are more Christianized than actually Christian. And it can complicate the efforts of evangelists.